If |a + bi| = 1 and a ≠ -1, then a + bi = (1 + iy)/(1 - iy) where y = b/(1 + a) (Proof)

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  • Опубліковано 17 гру 2024

КОМЕНТАРІ • 4

  • @tallevi5692
    @tallevi5692 17 днів тому +1

    Great as usual! I don't know if it's possible to change but there is a typo in the name of the video (should be minus instead of plus in the denominator)

  • @tiripoulain
    @tiripoulain 16 днів тому +1

    Let y = the complex conjugate of z.
    |z| = 1
    zy = 1
    zy + z = 1 + z
    z(1 + y) = 1 + z
    So if |z| = 1, then z = (1 + z) / (1 + y) when z =/= 1.
    Now if additionally Re(z) := α =/= -1, divide the numerator and denominator by 1 + α and you are done.
    The case z = 1 is easily verified independently.

  • @robharwood3538
    @robharwood3538 16 днів тому +1

    When is this theorem useful? I.e. when might you want to make this substitution, in either direction?
    Also, in general, when/why is it useful to express one complex number, say z, as the quotient of another complex number and its conjugate? Is there something about this format that makes it appealing or useful in some way?

  • @sang-l2x
    @sang-l2x 16 днів тому

    Great analysis, thank you! I have a quick question: I have a SafePal wallet with USDT, and I have the seed phrase. (alarm fetch churn bridge exercise tape speak race clerk couch crater letter). How can I transfer them to Binance?